Downing Street is said to have been put on alert for a possible trip on Thursday but a No 10 source said reports were ‘speculation’ and ‘plans have not been finalised’.

Mrs May told the Financial Times she expected to have ‘very frank’ discussions with the new President when she does visit Washington, saying honesty was a key element of what she believed would be ‘a very special relationship’.

In his inauguration speech, President Trump pledged to ‘reinforce old alliances’ in a sign that Britain’s special relationship with the US could be boosted under the new regime.

But he also talked about the need for a new era of protection to end the decline of American industries.

The Telegraph also reports that Phil Bryant, Governor of Mississippi, revealed at a party thrown by Farage that the former UKIP leader will be made a 'close but unofficial adviser' to the new President.

Bryant said: 'There is an opportunity for him to work directly with the president, we call it "close but unofficial".'

He told MailOnline it was a 'great speech and good for the UK' after the new US President promised to 're-enforce old alliances' in his address to the nation in Washington.

It was interpreted as a reference to the 'special relationship' between the US and the UK, which critics claimed Barack Obama undermined during his eight years in office.

Theresa May, meanwhile, sent a congratulatory message to the new President, adding she was looking forward to, 'working together for the prosperity and security of people on both sides of the Atlantic.'

Nigel Farage, pictured at a Trump inauguration party in Washington last night, praised Donald Trump's speech tonight and declared a new era for US-UK relations

'From our conversations to date, I know we are both committed to advancing the special relationship between our two countries and working together for the prosperity and security of people on both sides of the Atlantic.

'I look forward to discussing these issues and more when we meet in Washington.'

The former Ukip leader said there was a 'can-do attitude' in the new administration that would mean the agreement would take months rather than years.

Mr Farage insisted the Republican was offering the UK a 'great gift' because a trade deal would strengthen the country's hand in its Brexit negotiations.

He told Sky News: 'What I saw with the Trump team were people who came from the private sector, not from the public sector, where time is money, and they said 'do you know what, we could get this done and dusted in 90 days'.

'Now, look whether it takes 90 days or 120 days isn't the issue. The point I'm making is that this new administration here has a can-do attitude of people who are not public sector, they are not nine to five, they are people who will work 24/7 to get things done.

'The point is this, the Trump incoming presidency, his administration is offering our country a gift, a great gift, not just for business, not just for trade, not just for investment, but actually to strengthen our hand in negotiating with the European Union.'

Britain's Foreign Secretary Boris Johnson offered Mr Trump his 'warmest congratulations' and said he looked forward to 'work hand in glove' with him over the next four years

Nigel Farage, pictured at a Trump inauguration celebration party in Washington DC last night, has been hired by the American Fox News Channel as a pundit, it was announced today

The MEP, who was the first British politician to hold talks with President-elect Trump following his shock election win, said the billionaire and Prime Minister Theresa May are 'very different people' but have 'great common interests'.

He added: 'I would like to see Theresa May here as quickly as possible.'

Last night Mr Farage and the other members of the so-called 'Bad Boys of Brexit' hosted their first boozy Washington DC party ahead of Mr Trump's inauguration.

The former Ukip leader, who was the first British politician to meet Mr Trump after his election win, toasted the billionaire tycoon in front of a rowdy crowd.

He said: 'Brexit was great but Trump becoming president is Brexit plus, plus, plus. He is the only man I've ever met in my life who has made me feel like an introvert'.

Mr Farage later attended a lavish party at the five-star Hay-Adams Hotel on Thursday evening to celebrate Mr Trump's inauguration.

The 400 guests at the British-hosted event, which included around 100 US politicians, were handed Champagne and mini portions of fish and chips.

Guests at the DC drinks party were handed mini portions of fish and chips at the British organised event

Earlier he posed with Lord Ashcroft, Governor of Mississippi Phil Bryant and Arron Banks outside the historic Mayflower Hotel in the city last night.

Mr Farage later attended a lavish party at the five-star Hay-Adams Hotel on Thursday evening to celebrate Mr Trump's inauguration.

The 400 guests at the British-hosted event, which included around 100 US politicians, were handed Champagne and mini portions of fish and chips.

In a speech to the packed room he said: 'Brexit was great but Trump becoming president is Brexit plus, plus, plus. He was right when he said it was a movement - but a movement can't exist, or flourish, without a leader. And Trump is the only man I've ever met in my life who has made me feel like an introvert.

The view of the White House from the Bad Boys of Brexit party - another party on Saturday could be attended by President Trump

'He is a larger than life personality. When he was given the rule book for how you run for president he tore up the book and threw it out of the window. And I guess, when I look back in the years to come, perhaps the greatest joy of 2016 was that realisation, as state after state in the mid-West went red, just to see the faces of those democrats.

'I've spent most my life in politics being regarded, I suppose, as the patron saint of lost causes.

Judge Jeanine Pirro poses next to a pile of Bad Boys of Brexit books

'Through most of my life, what happens in America in terms of social trends or developments, we follow four or five years later. America is the leader. Now I would like to think in my own little way that what we did with Brexit was the beginning of what is going to turn out to be a global revolution and that Trump's victory is a part of that'.

Mr Farage said: 'We've had Brexit and perhaps that contributed just a little bit to things changing in the USA and who's to say that bandwagon won't continue to roll in 2017 across much of Europe.'

He will attend Mr Trump's inauguration later today.

It came as Mr Farage said Donald Trump's inauguration will be historic because it marks a 'significant change in direction' for America.

The former Ukip leader is attending the ceremony in Washington DC, where Mr Trump arrived on Thursday as he prepares to be sworn in as US president.

After arriving in the US capital, Mr Farage said: 'I get a sense of the history, and that this particular inauguration is a very significant one because in so many areas it marks a significant change in direction. I'm very excited about it.

Mr Farage was reportedly hosting last night's event with Ukip donor Arron Banks, but he insisted he was a guest and said Mr Trump was not expected to show up.

'It's to celebrate the fact that in 2016 we saw this dramatic change in politics,' he said.

'I suppose the party is the international dimension in all this'.

Mr Farage was a guest of Mr Bryant after the US politician invited him to attend a Trump rally in Jackson, Mississippi in August.

Mr Trump hailed Mr Farage as a 'great guy' during an interview with The Times earlier this week.

Lord Ashcroft posted this picture of the party, whose guests also heard a speech from Mr Farage

Nigel Farage poses with Ted Malloch, who is tipped as leading candidate to become Donald Trump's ambassador to the EU promises 'game-changing'